English

Braid variety cluster structures, I: 3D plabic graphs

Combinatorics 2024-05-31 v3 Algebraic Geometry Rings and Algebras Representation Theory

Abstract

We introduce 33-dimensional generalizations of Postnikov's plabic graphs and use them to establish cluster structures for type AA braid varieties. Our results include known cluster structures on open positroid varieties and double Bruhat cells, and establish new cluster structures for type AA open Richardson varieties.

Keywords

Cite

@article{arxiv.2210.04778,
  title  = {Braid variety cluster structures, I: 3D plabic graphs},
  author = {Pavel Galashin and Thomas Lam and Melissa Sherman-Bennett and David Speyer},
  journal= {arXiv preprint arXiv:2210.04778},
  year   = {2024}
}

Comments

v2: removed some arguments which appear in greater generality in the follow up paper arXiv:2301.07268. v3: Fixed minor typos

R2 v1 2026-06-28T03:09:45.299Z